Advertisements
Advertisements
Question
Solve the following differential equation:
`tan y ("d"y)/("d"x) = cos(x + y) + cos(x - y)`
Advertisements
Solution
The equation can be written as
`tan y ("d"y)/("d"x)` = cos(x + y) + cos(x – y)
W.K.T cos(A + B) + cos(A – B) = 2 cos A cos B
Here A = x, B = y
∴ `tan y ("d"y)/("d"x)` = 2 cos x cos y
`tany/cosy` dy = 2 cos x dx
Taking integration on both sides, we get
`int tany/cosy "d"y = 2int cos x "d"x`
`2 int tan y sec y "d"y = 2 int c x "d"x`
sec y = 2 sin x + C
APPEARS IN
RELATED QUESTIONS
The velocity v, of a parachute falling vertically satisfies the equation `"v" (dv)/(dx) = "g"(1 - v^2/k^2)` where g and k are constants. If v and are both initially zero, find v in terms of x
Find the equation of the curve whose slope is `(y - 1)/(x^2 + x)` and which passes through the point (1, 0)
Solve the following differential equation:
`y"d"x + (1 + x^2)tan^-1x "d"y`= 0
Solve the following differential equation:
`(x^3 + y^3)"d"y - x^2 y"d"x` = 0
Solve the following differential equation:
`y"e"^(x/y) "d"x = (x"e"^(x/y) + y) "d"y`
Solve the following differential equation:
`(y^2 - 2xy) "d"x = (x^2 - 2xy) "d"y`
Solve the following differential equation:
(x2 + y2) dy = xy dx. It is given that y (1) = y(x0) = e. Find the value of x0
Choose the correct alternative:
The solution of `("d"y)/("d"x) + "p"(x)y = 0` is
Choose the correct alternative:
The solution of `("d"y)/("d"x) = 2^(y - x)` is
Solve: ydx – xdy = 0 dy
Find the curve whose gradient at any point P(x, y) on it is `(x - "a")/(y - "b")` and which passes through the origin
Solve the following:
`("d"y)/(""dx) + y cos x = sin x cos x`
Solve the following:
If `("d"y)/("d"x) + 2 y tan x = sin x` and if y = 0 when x = `pi/3` express y in term of x.
Choose the correct alternative:
If y = ex + c – c3 then its differential equation is
Choose the correct alternative:
Solution of `("d"x)/("d"y) + "P"x = 0`
Choose the correct alternative:
A homogeneous differential equation of the form `("d"y)/("d"x) = f(y/x)` can be solved by making substitution
Choose the correct alternative:
The variable separable form of `("d"y)/("d"x) = (y(x - y))/(x(x + y))` by taking y = vx and `("d"y)/("d"x) = "v" + x "dv"/("d"x)` is
Solve `("d"y)/("d"x) = xy + x + y + 1`
